a rock is thrown from one side of a river to another. The function h (t) = -16t^2 + 80t + 30 gives the height in inches of the rock t seconds after it has been thrown.
Find h (2.5). \
What does h(2.5) represent in the context of this problem?
Does it make sense to find h (-10) in the context of this problem?
What is a reasonable domain given the context of this problem?
To find h(2.5), we simply plug in t = 2.5 into the given function:
h(2.5) = -16(2.5)^2 + 80(2.5) + 30
h(2.5) = -16(6.25) + 200 + 30
h(2.5) = -100 + 200 + 30
h(2.5) = 130 inches
This means that h(2.5) represents the height of the rock 2.5 seconds after it has been thrown.
It does not make sense to find h(-10) in the context of this problem because time cannot be negative in this situation. The rock cannot exist before it has been thrown.
A reasonable domain for this problem would be t ≥ 0, since time should be non-negative in the context of the problem.